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We have presented a theoretical study of the electrical conductance properties of molecular wires in the context of one-electron theory. A numerical method has been developed for the study of transport in molecular wires which solves for the transmission coefficients using Schroedinger's equation. It allows for the study of multimode leads attached to a molecule. We then proceeded to present a simple analytically solvable model which highlighted the interesting phenomena of antiresonances. A formula was derived that predicts Fermi energies for which a molecule with a given set of molecular energy levels should display antiresonances. It predicts two mechanisms by which antiresonances arise: one due to interference between the molecular orbitals and the other due to a cancellation of the effective hopping parameter.

As an application of our numerical method studied the conductance of BDT. We examined the role of coupling by considering both the strong and weak regimes. For strong coupling it was found that the MW has regions of strong transmission. These regions occur at energies which differ from the isolated molecule's energy levels because of state hybridization with the surface states of the gold tips. The conductance found for the strong coupling case was orders of magnitude greater than that found experimentally, although qualitatively it shared common features. In the weak coupling study the transmission displayed resonances at energies corresponding to those of the isolated molecule. The magnitude was also significantly down. This resulted in a conductance curve that was of the magnitude found in the experiment. Future work will need to focus on the electrostatic problem of the molecule within an applied electric field and the consequences of this in the context of Landauer theory, many-electron and possible polaronic effects within the MW.

Using our analytic formula for antiresonances, we were able to predict the occurrence of an antiresonance within a more sophisticated numerical study utilizing a molecule attached bridging a metal wire break junction. The model should also be of interest for future MW work since it introduces the idea of ``filter'' molecules. Our numerical studies showed that $\pi $conjugated chain molecules act as effective mode filters to electrons incident from the metallic leads. The filter chains in our model reduced the number of propagating modes down to one, which was then coupled to the ``active'' molecule. Our formula was derived on the assumption of only a single propagating mode, and for the ``active'' molecule considered it was able to successfully predict the energy at which the antiresonance occurred. The antiresonance was charaterized by a drop in the differential conductance.

Next: Bibliography Up: Electrical Conductance of Molecular Previous: Antiresonance Calculations
Eldon Emberly

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